Properties

Label 912.2.k
Level $912$
Weight $2$
Character orbit 912.k
Rep. character $\chi_{912}(607,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $8$
Sturm bound $320$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(320\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

Total New Old
Modular forms 172 20 152
Cusp forms 148 20 128
Eisenstein series 24 0 24

Trace form

\( 20q + 20q^{9} + O(q^{10}) \) \( 20q + 20q^{9} + 20q^{25} + 20q^{49} + 4q^{57} + 56q^{61} + 8q^{73} - 24q^{77} + 20q^{81} - 24q^{85} + 56q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
912.2.k.a \(2\) \(7.282\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(-4\) \(0\) \(q-q^{3}-2q^{5}+2\beta q^{7}+q^{9}-\beta q^{11}+\cdots\)
912.2.k.b \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+2\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
912.2.k.c \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(6\) \(0\) \(q-q^{3}+3q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
912.2.k.d \(2\) \(7.282\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(-4\) \(0\) \(q+q^{3}-2q^{5}-2\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
912.2.k.e \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-2\zeta_{6}q^{7}+q^{9}-2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
912.2.k.f \(2\) \(7.282\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(6\) \(0\) \(q+q^{3}+3q^{5}-\zeta_{6}q^{7}+q^{9}+3\zeta_{6}q^{11}+\cdots\)
912.2.k.g \(4\) \(7.282\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-4\) \(-2\) \(0\) \(q-q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
912.2.k.h \(4\) \(7.282\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(4\) \(-2\) \(0\) \(q+q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)